论文标题
混合光滑度主导的空间中白噪声的样品路径
Sample Paths of White Noise in Spaces with Dominating Mixed Smoothness
论文作者
论文摘要
事实证明，白噪声的样本路径是某些BESOV空间的元素，具有主导的混合光滑度。与各向同性空间不同，随着空间维度的增加，规律性不会变得更糟。因此，在各向同性空间中，白噪声实际上比已知的尖锐规律性更平滑得多。我们的技术的应用为带边界噪声的半空间上的泊松和热方程式的规律带来了新的结果。主要的新颖性是对边界的奇异性与切线，正常和时间方向的平滑度之间的相互作用的灵活处理。
The sample paths of white noise are proved to be elements of certain Besov spaces with dominating mixed smoothness. Unlike in isotropic spaces, here the regularity does not get worse with increasing space dimension. Consequently, white noise is actually much smoother than the known sharp regularity results in isotropic spaces suggest. An application of our techniques yields new results for the regularity of solutions of Poisson and heat equation on the half space with boundary noise. The main novelty is the flexible treatment of the interplay between the singularity at the boundary and the smoothness in tangential, normal and time direction.
